Express your answer as a mixed number simplified to lowest terms. $3\dfrac{4}{7}-1\dfrac{2}{3} = {?}$
Solution: Find a common denominator for the fractions: $= {3\dfrac{12}{21}}-{1\dfrac{14}{21}}$ Convert ${3\dfrac{12}{21}}$ to ${2 + \dfrac{21}{21} + \dfrac{12}{21}}$ So the problem becomes: ${2\dfrac{33}{21}}-{1\dfrac{14}{21}}$ Separate the whole numbers from the fractional parts: $= {2} + {\dfrac{33}{21}} - {1} - {\dfrac{14}{21}}$ Bring the whole numbers together and the fractions together: $= {2} - {1} + {\dfrac{33}{21}} - {\dfrac{14}{21}}$ Subtract the whole numbers: $=1 + {\dfrac{33}{21}} - {\dfrac{14}{21}}$ Subtract the fractions: $= 1+\dfrac{19}{21}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{19}{21}$